To find the total surface area of the figure, first calculate the surface area of each rectangular prism separately.
For the smaller rectangular prism:
- Front and back faces: 10mm x 8mm = 80mm^2 (x2 for both faces)
- Top and bottom faces: 10mm x w = 10w mm^2 (2w for both faces)
- Left and right side faces: 8mm x w = 8w mm^2 (2w for both faces)
Total surface area for smaller prism: 160 + 10w + 8w = 160 + 18w mm^2
For the larger rectangular prism:
- Front and back faces: 6mm x 6mm = 36mm^2 (x2 for both faces)
- Top and bottom faces: 6mm x 6mm = 36mm^2 (x2 for both faces)
- Left and right side faces: 6mm x 6mm = 36mm^2 (x2 for both faces)
Total surface area for larger prism: 72 + 72 + 72 = 216 mm^2
Now add the surface areas of both prisms together:
Surface area = 160 + 18w + 216
Surface area = 376 + 18w mm^2
Since the combined length of the two rectangular prisms measures 16 millimeters, w = 16 - 10 = 6 mm
Surface area = 376 + 18(6)
Surface area = 376 + 108
Surface area = 484 mm^2
Therefore, the total surface area of the figure is 484 mm^2.
Use the image to answer the question.
An illustration shows a three dimensional composite figure formed by a smaller rectangular prism connected to a larger rectangular prism. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism on the left has a length of 10 millimeters a height of 8 millimeters. The width of the rectangular prism is not shown, but it aligns perfectly with the width of the rectangular prism on the right. The rectangular prism on the right has a length of 6 millimeters, a width of 6 millimeters, and a height 6 of millimeters. The combined length of the two rectangular prisms measures 16 millimeters.
What is the total surface area of the figure?
(1 point)
mm2
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nnnooooooooo
I'm sorry for the mistake in my previous response. Let me correct that calculation.
The total surface area of the figure can be found by calculating the surface area of each face of the two rectangular prisms and adding them together.
For the smaller rectangular prism:
- Front and back faces: 10mm x 8mm = 80mm^2 (x2 for both faces)
- Top and bottom faces: 10mm x 6mm = 60mm^2 (x2 for both faces)
- Left and right side faces: 8mm x 6mm = 48mm^2 (x2 for both faces)
Surface area of smaller prism: 2(80) + 2(60) + 2(48) = 160 + 120 + 96 = 376 mm^2
For the larger rectangular prism:
- Front and back faces: 6mm x 6mm = 36mm^2 (x2 for both faces)
- Top and bottom faces: 6mm x 6mm = 36mm^2 (x2 for both faces)
- Left and right side faces: 6mm x 8mm = 48mm^2 (x2 for both faces)
Surface area of larger prism: 2(36) + 2(36) + 2(48) = 72 + 72 + 96 = 240 mm^2
Total surface area of the figure: 376 + 240 = 616 mm^2
Therefore, the total surface area of the composite figure is 616 mm^2. Thank you for your patience.
The total surface area of the figure can be found by calculating the surface area of each face of the two rectangular prisms and adding them together.
For the smaller rectangular prism:
- Front and back faces: 10mm x 8mm = 80mm^2 (x2 for both faces)
- Top and bottom faces: 10mm x 6mm = 60mm^2 (x2 for both faces)
- Left and right side faces: 8mm x 6mm = 48mm^2 (x2 for both faces)
Surface area of smaller prism: 2(80) + 2(60) + 2(48) = 160 + 120 + 96 = 376 mm^2
For the larger rectangular prism:
- Front and back faces: 6mm x 6mm = 36mm^2 (x2 for both faces)
- Top and bottom faces: 6mm x 6mm = 36mm^2 (x2 for both faces)
- Left and right side faces: 6mm x 8mm = 48mm^2 (x2 for both faces)
Surface area of larger prism: 2(36) + 2(36) + 2(48) = 72 + 72 + 96 = 240 mm^2
Total surface area of the figure: 376 + 240 = 616 mm^2
Therefore, the total surface area of the composite figure is 616 mm^2. Thank you for your patience.
um noo
I apologize for the error again. Let's try to solve it correctly this time.
The total surface area of the composite figure can be calculated by finding the surface area of each face and adding them together.
For the smaller rectangular prism:
- Front and back faces: 10mm x 8mm = 80mm^2 (x2 for both faces)
- Top and bottom faces: 10mm x 6mm = 60mm^2 (x2 for both faces)
- Left and right side faces: 8mm x 6mm = 48mm^2 (x2 for both faces)
Surface area of the smaller prism: 2(80) + 2(60) + 2(48) = 160 + 120 + 96 = 376 mm^2
For the larger rectangular prism:
- Front and back faces: 6mm x 6mm = 36mm^2 (x2 for both faces)
- Top and bottom faces: 6mm x 6mm = 36mm^2 (x2 for both faces)
- Left and right side faces: 6mm x 8mm = 48mm^2 (x2 for both faces)
Surface area of the larger prism: 2(36) + 2(36) + 2(48) = 72 + 72 + 96 = 240 mm^2
Total surface area of the figure: 376 + 240 = 616 mm^2
Therefore, the correct total surface area of the composite figure is 616 mm^2. Thank you for your patience.
The total surface area of the composite figure can be calculated by finding the surface area of each face and adding them together.
For the smaller rectangular prism:
- Front and back faces: 10mm x 8mm = 80mm^2 (x2 for both faces)
- Top and bottom faces: 10mm x 6mm = 60mm^2 (x2 for both faces)
- Left and right side faces: 8mm x 6mm = 48mm^2 (x2 for both faces)
Surface area of the smaller prism: 2(80) + 2(60) + 2(48) = 160 + 120 + 96 = 376 mm^2
For the larger rectangular prism:
- Front and back faces: 6mm x 6mm = 36mm^2 (x2 for both faces)
- Top and bottom faces: 6mm x 6mm = 36mm^2 (x2 for both faces)
- Left and right side faces: 6mm x 8mm = 48mm^2 (x2 for both faces)
Surface area of the larger prism: 2(36) + 2(36) + 2(48) = 72 + 72 + 96 = 240 mm^2
Total surface area of the figure: 376 + 240 = 616 mm^2
Therefore, the correct total surface area of the composite figure is 616 mm^2. Thank you for your patience.